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Accuracy and simplicity of analytical expressions for the relations between frequency and critical bandwidth as well as critical-band rate (in Bark) are assessed for the purpose of applications in speech perception research and in speech technology. The equivalent rectangular bandwidth (ERB) is seen as a measure of frequency resolution, while the classical critical-band rate is considered a measure of tonotopic position. For the conversion of frequency to critical-band rate, and vice versa, the inversible formula z=26.81/(1+1960/f )−0.53 is proposed. Within the frequency range of the perceptually essential vowel formants (0.2–6.7 kHz), it agrees to within ±0.05 Bark with the Bark scale, originally published in the form of a table.
Hartmut Traunmüller (Sun,) studied this question.